Page 127 - Materials Chemistry, Second Edition

110 Practical Design Calculations for Groundwater and Soil Remediation

The ratio between the free air and liquid diffusion coefficients
= (0.089) ÷ (1.02 × 10 ) = 8,720
−5
(b) The MW of toluene (C H CH ) is 92, and the MW of benzene
3
5
6
(C H ) is 78.
6
6
Use Equation (3.41) to determine the diffusion coefficient:
(0.089) 92
D 1
= =
D 2 D 2 78
So the diffusion coefficient of toluene at 20°C = 0.082 cm /s.
2
Discussion:
1. The diffusion coefficient of benzene in free air is 8,720 higher
than that in the dilute aqueous phase.
2. The diffusion coefficient of toluene estimated from that of ben-
zene and the molecular weight relationship (0.082 cm /s) is
2
essentially the same as that in Table 2.5 (0.083 cm /s).
2

3.6.3 Retardation Factor for COC Vapor Migration in the Vadose Zone
For an air stream flowing through a porous medium, the gas-phase retarda-
tion factor can be derived as [9]

R =+ ρ b K p + φ w (3.43)
1
a
φ a H φ a H
where ρ is the dry bulk density, K is the soil–water partition coefficient, H
p
b
is the Henry’s constant, ϕ is the air-filled porosity, and ϕ is the volumetric
w
a
water content.
This retardation factor will be a constant if ϕ does not change. It is analo-
w
gous to the retardation factor, R, for the movement of COCs in an aquifer.
The movement of the COC in the void of the vadose zone will be retarded
by a factor of R . The second term on the right-hand side of Equation (3.43)
a
represents the partitioning of the COCs between the vapor phase, the soil
moisture phase, and the solid phase. The third term represents the partition-
ing between the vapor phase and the solid phase. As the COC in the vapor
phase moves through the air-filled pores, the migration rate of the COC in
the air is slower than that of the air itself, because of the loss of its mass to the
soil moisture and to the soil organic carbon.
Under the condition of no advective flow, the gas-phase retardation factor
can be defined as the ratio of the diffusion rate of an inert compound such
as nitrogen to the diffusion rate of the COC. Under advective flow, it can be